Effectiveness of Measures of Performance During Speculative Bubbles

TL;DR

This paper evaluates the stability of performance measures based on maximum drawdown during speculative bubbles, especially when the underlying financial process deviates from Brownian motion, using both theoretical and empirical data.

Contribution

It investigates the robustness of drawdown-based performance measures under fractional Brownian motion and real market data during bubbles, highlighting their effectiveness.

Findings

Performance measures remain stable under fractional Brownian motion.

Empirical analysis confirms measure reliability during speculative bubbles.

Deviation from Brownian motion affects traditional financial assumptions.

Abstract

Statistical analysis of financial data most focused on testing the validity of Brownian motion (Bm). Analysis performed on several time series have shown deviation from the Bm hypothesis, that is at the base of the evaluation of many financial derivatives. We inquiry in the behavior of measures of performance based on maximum drawdown movements (MDD), testing their stability when the underlying process deviates from the Bm hypothesis. In particular we consider the fractional Brownian motion (fBm), and fluctuations estimated empirically on raw market data. The case study of the rising part of speculative bubbles is reported.